The effectiveness and accuracy of signal receiving devices can be impaired by undesirable interference and noise. Such undesirable interference can be particularly disruptive in signal receiving devices that receive and process location-determining signals, such as the signals generated by the Global Positioning System constellation of satellites. Undesirable interference in these signals can cause errors in the operation of receivers, potentially reducing the sensitivity, accuracy and effectiveness of the receivers. In general, when a receiver receives a signal that can be used to determine the location of the receiver, the signal may be corrupted by various types of interference. Some interference may be white or broadband noise. Standard matched filtering and testing by means of correlation calculations performs well when the noise is nearly white. If standard correlation techniques are used in the presence of significant narrowband noise, then the noise alone can often cause false correlation peaks. These peaks will occur much more frequently than a model based on pure white noise would predict. With relatively strong location determining signals, this does not pose a major issue since these peaks still tend to be much lower than the true correlation peaks coming from the actual signals. However, if it is desired to extend sensitivity into the much lower SNR regimes, then the peaks from narrowband noise can result in false-positives that turn into completely erroneous satellite acquisitions and then into erroneous locations. Also, at these lower SNRs, the narrowband noise induced correlations can cause significant apparent local movement in the position of true correlation peaks. This translates into larger than expected position errors. Often, there can be significant amounts of narrowband noise. Narrowband noise can be caused by, for example, interference from other devices or by operation of the receiving device itself. Such noise can have a detrimental effect on the processing of the received signal, potentially resulting in substantial errors in determining the location of the receiver. It is desirable to mitigate the effects of narrowband noise before further processing of such signals.
One approach to removing such noise is to form the Fourier transform (or, in the case of sampled data, the fast Fourier transform) of a received signal, identify the noisy frequencies as those having unusually large values, and remove the corresponding frequency components from the signal. Unfortunately, however, this approach is computationally intensive, particularly when the received signal is long. It would be desirable to provide a system and method that allows computationally efficient identification and removal of narrowband noise, or alternatively, is robust to the effects of narrowband noise
Other techniques for removing narrowband noise rely on the use of various types of adaptive notch filters, which often require time-domain processing of the signal. Such techniques are undesirable at least because they may require a large number of such filters (particularly where there are multiple sources of noise). Further, if the signal to be filtered has a limited duration, an adaptive filter may have insufficient exposure to the signal to tune itself to the frequencies that require notching. With the exact identification of the spectral characteristics of narrowband noise, and an estimate of the signal power, standard Bayesian techniques can be used to optimally weigh the signal components in a detection algorithm without having to directly modify the noisy signal. However, such techniques rely on knowing both the detailed characteristics of the noise (such as assuming Gaussianity) and in having an estimate of signal power available. However, in the case of location-determining signals, there can be a very wide range of possible signal powers and in general an estimate for signal power will only be available after detection has already succeeded.
Accordingly, there is a need for a system and method that allows the efficient and accurate identification and removal of undesirable frequencies in a computationally efficient manner.